The first theorem of this kind, namely when \(n=2\)  and
\(\alpha _1=\alpha _2={1\over \sqrt{2}}\) , was proved by G. Pólya in 1923.
Subsequently, the characterization of the Gaussian distribution on the real
line by the property of equidistribution of two linear forms of
independent identically distributed random variables were studied by
I. Marcinkiewicz, Yu. V. Linnik, A.A. Zinger and others
(see [1]}).
